Use Cramer's rule to determine if the system is inconsistent system or contains dependent equations.
2x + y = 8
6x + 3y = 24
A. system is inconsistent
B. system contains dependent equations
b ?
4 answers
Yes it's B, since it can be seen clearly that the simplified version of the second equation is equal to the first equation.
note the determinant of
2 1
6 3
is 6 - 6 = 0
therefore the solutions using Cramer's Rule are undefined
2 1
6 3
is 6 - 6 = 0
therefore the solutions using Cramer's Rule are undefined
thank you guys :)
the solution would be:
( det 8 1 det 2 8
24 3 6 24
_____ ______
det 2 1 2 1
6 3 , 6 3 )
which is (0/0, 0/0) The zero in the denominator indicates that the system can not be solved using cramer's rule and is therefore not consistent and independent.
I have not read this but would conjecture that The zeros in the numerator indicate
that the system is consistent and dependent.
( If it were an inconsistent system, we would expect that both numerators would be non-zero, and not equal to each other)
( det 8 1 det 2 8
24 3 6 24
_____ ______
det 2 1 2 1
6 3 , 6 3 )
which is (0/0, 0/0) The zero in the denominator indicates that the system can not be solved using cramer's rule and is therefore not consistent and independent.
I have not read this but would conjecture that The zeros in the numerator indicate
that the system is consistent and dependent.
( If it were an inconsistent system, we would expect that both numerators would be non-zero, and not equal to each other)